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Prime-Interval Algebras
Joseph M. Shunia
Starting from a positive integer and no a priori information about the primes above it, we construct a polynomial quotient ring that recovers exactly the primes in fro…
Elementary closed-forms for non-trivial divisors
Mihai Prunescu, Joseph M. Shunia
We present several elementary closed-forms that express a non-trivial divisor for every composite integer . Each closed-form consists of a fixed number of elementary arithme…
On modular representations of C-recursive integer sequences
Mihai Prunescu, Joseph M. Shunia
Prunescu and Sauras-Altuzarra showed that all C-recursive sequences of natural numbers have an arithmetic div-mod representation that can be derived from their generating function.…
On arithmetic terms expressing the prime-counting function and the n-th prime
Mihai Prunescu, Joseph M. Shunia
We present the first fixed-length elementary closed-form expressions for the prime-counting function, , and the -th prime number, . These expressions are arithmetic…
Arithmetic-term representations for the greatest common divisor
Mihai Prunescu, Joseph Shunia
We construct a new arithmetic-term representation for the function gcd(a,b). As a byproduct, we also deduce a representation gcd(a,b) by a modular term in integer arithmetic.